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Numerical analysis of quasilinear parabolic equations under low regularity assumptions

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In this paper, we carry out the numerical analysis of a class of quasilinear parabolic equations, where the diffusion coefficient depends on the solution of the partial differential equation. The goal is to prove error estimates for the fully discrete equation using discontinuous Galerkin discretization in time DG(0) combined with piecewise linear finite elements in space. This analysis is performed under minimal regularity assumptions on the data. In particular, we omit any assumption regarding existence of a second derivative in time of the solution.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada y Ciencias de la Computación, E.T.S.I. Industriales y de Telecomunicación, Universidad de Cantabria, Av. Los Castros s/n, 39005, Santander, Spain

    Eduardo Casas

  2. Department of Mathematics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Zografou Campus, 15780, Athens, Greece

    Konstantinos Chrysafinos

  3. IACM, FORTH, 20013, Heraklion, Crete, Greece

    Konstantinos Chrysafinos

Authors
  1. Eduardo Casas
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  2. Konstantinos Chrysafinos
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Correspondence to Konstantinos Chrysafinos.

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The first author was partially supported by Spanish Ministerio de Economía, Industria y Competitividad under research projects MTM2014-57531-P and MTM2017-83185-P.

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Casas, E., Chrysafinos, K. Numerical analysis of quasilinear parabolic equations under low regularity assumptions. Numer. Math. 143, 749–780 (2019). https://doi.org/10.1007/s00211-019-01071-5

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